Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×C4⋊C16 ⋊ C2 |
| Sylow | C53 ⋊ #2206 |
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^52,e^c=ef,f^c=fg,h^c=h^521069 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27297517, #27297518, #27297538, … |
| maximal normal subgroup of | #27297517, #27297518, #27297538, … |
| maximal quotient of | #27298209, #27298265, #27298384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6546);